Simplify to lowest terms. $\dfrac{60}{90}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 60 and 90? $60 = 2\cdot2\cdot3\cdot5$ $90 = 2\cdot3\cdot3\cdot5$ $\mbox{GCD}(60, 90) = 2\cdot3\cdot5 = 30$ $\dfrac{60}{90} = \dfrac{2 \cdot 30}{ 3\cdot 30}$ $\hphantom{\dfrac{60}{90}} = \dfrac{2}{3} \cdot \dfrac{30}{30}$ $\hphantom{\dfrac{60}{90}} = \dfrac{2}{3} \cdot 1$ $\hphantom{\dfrac{60}{90}} = \dfrac{2}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{60}{90}= \dfrac{2\cdot30}{2\cdot45}= \dfrac{2\cdot 3\cdot10}{2\cdot 3\cdot15}= \dfrac{2\cdot 3\cdot 5\cdot2}{2\cdot 3\cdot 5\cdot3}= \dfrac{2}{3}$